An unbiased coin is tossed six times in a row. Which statement describing the last two coin tosses has the highest probability of being correct?

$B$ is correct here. It has probability $\frac12$ in contrast to the other options that all have probability $\frac14$.

A) TT has probability $\frac14$

B) HT or TH has probability $\frac14+\frac14$ (summation of two probabilities of mutually exclusive events)

C) HH has probability $\frac14$

D) HT has probability $\frac14$

Essential for this conclusion is the fact that the coin is unbiased.

A is not correct; B is. Statistical regularity – more often called independence – means that

• the results of the three previous trials do not affect the fourth trial's outcomes
• the four prior tosses of the coin in the fourth trial do not affect the last two tosses

Therefore, each of $\text{HH, HT, TH, TT}$ has a $\frac14$ chance of occurring. With regards to the options, only option B has a $\frac12$ chance; the others have a $\frac14$ chance.